Most of exchange platforms provide the possibility of withdrawing Matic with zero fees.
Not free on all exchanges for withdrawal, details are available on
Withdrawalfees.comMatic use manly because of low fees so I do not think that a person with some cryptos will be unable to pay 1 dollars to buy some Matic, which may be considered enough for many transfers.
I agree with you. If I want to use a chain with swap feature, I will allocate a number of coins to use as transaction fee, swap fee: on BSC, it's BNB; on ERC20, it's ETH, and so on.
To avoid getting troubles, don't click on Max button when you swap.